Robust Stability of Genetic Regulatory Networks with Stochastic Time Delays Under Intrinsic and Extrinsic Noises

Gene regulation is inherently a stochastic process due to intrinsic and extrinsic noises which cause the fluctuations and uncertainties of kinetic parameters. On the other hand, time delays are usually inevitable due to different biochemical reactions in the genetic regulatory networks (GRNs) which are also affected by noises. Therefore, in this paper, we propose a GRN model that is subject to additive and multiplicative noises as well as random time delays. Robust stochastic stability of such GRNs with disturbance attenuation is analyzed by applying the control theory and mathematical tools. Based on the Lyapunov method, new stability conditions are derived in the form of linear matrix inequalities (LMIs) that are dependent on the statistical properties of stochastic time-delays. An example is employed to illustrate the applicability and usefulness of the developed theoretical results.